If you know a way to operate a transformer without connecting it to a voltage source (e.g. mains power supply), I'll think about to the specific problem.
If part of the primary is shortted then the net effect is reduced number of turns on the primary causing more flux on the core (core can saturate loosing its magetic properties) & more peak primary current which will damage the winding after few Secs / min depending upon how many turns are shorted out.
If part of the primary is shortted then the net effect is reduced number of turns on the primary causing more flux on the core (core can saturate loosing its magetic properties) & more peak primary current which will damage the winding after few Secs / min depending upon how many turns are shorted out.
Meaning that when the primary side of the transformer is short circute it reduce the resistance of the primary coil and can burn the transformer in few second.